Long-distance bus from Wuhan (Hankou) train station to Lushan mountains/Gulin street?

For Lushan, do you mean the one in Jiangxi Province?
If so, you need to walk to the Jinjiadun Long-distance Bus Station to take a bus for Jiujiang first. The buses for Jiujiang start at around 06:50.
Upon reaching Jiujiang Bus Station, you can find the direct buses for that mountain.

Great! Do you know how often the buses go? And how long the bus trip takes?

Buses from Jinjiadun Bus Station to Jiujiang are scheduled from 06:50 to 17:00 every half an hour!

Here I have a better way for you: upon getting to Hankou Train Station, transfer to another train to Lushan directly in 2.5h. At Lushan Train Station, there are direct shuttle buses to the scenic area!